Background: Our study aimed to assess the differences between domestic and international students in terms of social support, vital exhaustion, and depression during the time of COVID-19. Methods: The online cross-sectional survey was conducted via Google Forms® at three time intervals during the pandemic. Results: Respectively 1320, 246, and 139 students completed our questionnaires in the different time intervals. International students reported significantly lower values of perceived social support. Women reached higher scores regarding vital exhaustion in both samples. Concerning depression, international female students had higher values than their male counterparts but the difference diminished with time. No differences could be found in the comparison of depression between domestic female and male students. Significant correlations were found between depression, perceived social support, and vital exhaustion. Discussion: International students perceive diminished social support just when they need more. Decreased levels of perceived social support may contribute to the development of their psychological problems.